The geometry of a battery cooling system has a direct influence on cell temperature, temperature uniformity, pressure loss, and the energy required to circulate the coolant. This review examines recent approaches used to optimize liquid-cooled structures for electric vehicle battery packs, with particular attention to channel layout, manifold configuration, contact geometry, and plate dimensions. Parametric studies remain useful for identifying influential variables and explaining the physical behavior of a design. For problems involving several interacting parameters, multi-objective algorithms and surrogate models provide a more practical alternative to repeated high-cost CFD simulations. Recent studies also show growing interest in bio-inspired channels and topology optimization, which can generate unconventional flow paths but often introduce manufacturing and validation difficulties. Across the reviewed work, the most reliable designs are those evaluated against both thermal and hydraulic criteria and subsequently rechecked using the original numerical model or experiments. Based on these findings, a structured design procedure is discussed, covering problem definition, variable screening, numerical validation, sampling, surrogate construction, Pareto optimization, and final verification. Future research should place greater emphasis on robust designs that remain effective under changing operating conditions and can be manufactured and integrated at module or pack level.